CALC The position of a particle between and is given by

Chapter 2, Problem 2.57

(choose chapter or problem)

The position of a particle between t = 0 and t = 2.00 s is given by \(x(t)=\left(3.00\mathrm{\ m}/\mathrm{s}^3\right)t^3-\left(10.0\mathrm{\ m}/\mathrm{s}^2\right)t^2+(9.00\mathrm{\ m}/\mathrm{s})t\). (a) Draw the \(x-t,\ v_x-t\), and \(a_x-t\) graphs of this particle. (b) At what time(s) between t = 0 and t = 2.00 s is the particle instantaneously at rest? Does your numerical result agree with the \(v_x-t\) graph in part (a)? (c) At each time calculated in part (b), is the acceleration of the particle positive or negative? Show that in each case the same answer is deduced from \(a_{x}(t)\) and from the \(v_x-t\) graph. (d) At what time(s) between t = 0 and t = 2.00 s is the velocity of the particle instantaneously not changing? Locate this point on the \(v_x-t\) and \(a_x-t\) graphs of part (a). (e) What is the particle's greatest distance from the origin (x = 0) between t = 0 and t = 2.00 s? (f) At what time(s) between and is the particle speeding up at the greatest rate? At what time(s) between t = 0 and t = 2.00 s is the particle slowing down at the greatest rate? Locate these points on the \(v_x-t\) and \(a_x-t\) graphs of part (a).